To study the DMT in MIMO-NOMA channels, we assume that the power allocation coefficients scale as \({\zeta _{m,k}} \simeq {c_{m,k}}{{\bar{\gamma }}^{ - {\upsilon _{m,k}}}}\) , where \({c_{m,k}}\)  is a constant and \({\upsilon _{m,k}}\ge 0\) . In particular, the power allocation scheme can be treated as a fixed one if \({\upsilon _{m,k}}=0\)  for all \(m\in [1,M]\)  and \(k\in [1,K]\) . To reap the multiplexing benefit of MIMO-NOMA channels, let the transmission rate for the data stream of \(x_{m,k}\)  scale as \({R_{m,k}} = {r_{m,k}}{\log _2}\bar{\gamma }\) , where \({r_{m,k}}\ge 0\)  corresponds to multiplexing gain [1]}. On the scale of interest, by following the above settings together with \({\theta _{m,k}}>0\)  and \(\sum \nolimits _{k = 1}^K {{\zeta _{m,k}}} = {1}/{M}\) , the conditions of \({\upsilon _{m,1}} \ge \cdots \ge {\upsilon _{m,K}} = 0\)  and \({r_{m,i}} \le {\upsilon _{m,i - 1}} - {\upsilon _{m,i}}\)  for \(2 \le i \le K\)  must be satisfied. Accordingly, on the basis of (REF ) and (REF ), the outage probability \(p_{m,k}^{out}\)  at target transmission rates \({R_{m,1}},\cdots ,{R_{m,K}}\)  is proportional to
\(p_{m,k}^{out} &\propto {\left( {{{\bar{\gamma }{\theta _{m,k}}}}} \right)^{-({N_r} - M + 1)}} \\&\propto {\left( {{{\bar{\gamma }\min \left\lbrace  {{c_{m,i}}{{\bar{\gamma }}^{ - {\upsilon _{m,i}} - {r_{m,i}}}},k \le i \le K} \right\rbrace }}} \right)^{-({N_r} - M + 1)}}\\&\propto {{\bar{\gamma }}^{-\left( {{N_r} - M + 1} \right)\left( {1 - {\upsilon _{m,k}} - {r_{m,k}}} \right)}},\) 
